The Canonical Coset Decomposition of Unitary Matrices Through Householder Transformations

TL;DR

This paper explores the relationship between the canonical coset decomposition and Householder reflections of unitary matrices, providing a way to parametrize such matrices using Householder transformations.

Contribution

It establishes a connection between coset decomposition and Householder reflections, enabling new parametrization methods for unitary matrices.

Findings

Derived the relation between coset decomposition and Householder reflections.

Proposed a parametrization method for unitary matrices using Householder transformations.

Facilitated new approaches for matrix decomposition in quantum computing and signal processing.

Abstract

This paper reveals the relation between the canonical coset decomposition of unitary matrices and the corresponding decomposition via Householder reflections. These results can be used to parametrize unitary matrices via Householder reflections.